Thouless-Anderson-Palmer equations for generic p-spin glasses

Antonio Auffinger; Aukosh Jagannath

doi:10.1214/18-AOP1307

Thouless-Anderson-Palmer equations for generic p-spin glasses

Antonio Auffinger, Aukosh Jagannath

Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

We study the Thouless-Anderson-Palmer (TAP) equations for spin glasses on the hypercube. First, using a random, approximately ultrametric decomposition of the hypercube, we decompose the Gibbs measure, 〈·〉_N, into a mixture of conditional laws, 〈·〉_α,N . We show that the TAP equations hold for the spin at any site with respect to 〈·〉_α,N simultaneously for all α. This result holds for generic models provided that the Parisi measure of the model has a jump at the top of its support.

Original language	English (US)
Pages (from-to)	2230-2256
Number of pages	27
Journal	Annals of Probability
Volume	47
Issue number	4
DOIs	https://doi.org/10.1214/18-AOP1307
State	Published - 2019

Funding

Keywords

Cluster decomposition
Random measures
Spin glasses
TAP
Ultrametricity

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/18-AOP1307

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abstract = "We study the Thouless-Anderson-Palmer (TAP) equations for spin glasses on the hypercube. First, using a random, approximately ultrametric decomposition of the hypercube, we decompose the Gibbs measure, 〈·〉N, into a mixture of conditional laws, 〈·〉α,N . We show that the TAP equations hold for the spin at any site with respect to 〈·〉α,N simultaneously for all α. This result holds for generic models provided that the Parisi measure of the model has a jump at the top of its support.",

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AU - Jagannath, Aukosh

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AB - We study the Thouless-Anderson-Palmer (TAP) equations for spin glasses on the hypercube. First, using a random, approximately ultrametric decomposition of the hypercube, we decompose the Gibbs measure, 〈·〉N, into a mixture of conditional laws, 〈·〉α,N . We show that the TAP equations hold for the spin at any site with respect to 〈·〉α,N simultaneously for all α. This result holds for generic models provided that the Parisi measure of the model has a jump at the top of its support.

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KW - Random measures

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KW - Ultrametricity

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Thouless-Anderson-Palmer equations for generic p-spin glasses

Abstract

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Keywords

ASJC Scopus subject areas

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